Answer
$P(t)=200(0.98)^{t}$
Work Step by Step
We define our variables as
$P(t)=\text{Population of animals}$
$t=\text{Time in years}$
Since the shrinking started with $200$ animals, in our model,
$a=200$.
The population is shrinking. So, the growth rate will be represented by a negative number.
The growth or decay rate $r$ is $-2\%=-0.02$
We can find the base using the formula
$b=1+r$
$b=1+(-0.02)=0.98$
Exponential model is of the form $P(t)=a\cdot b^{t}$
Therefore, our model is $P(t)=200(0.98)^{t}$
